Q4.  (i) m & n are two integers such that m=n2-n.  Show that m2-2m is divisible by 24.

(ii) If x & y are two positive numbers such that x + y = 1, find maximum value of x4y + xy4.

Solution :

 (i) m = n2-n (Given)

So, m2 – 2m        =  n2(n-1)2   - 2n(n-1)

                                = n(n-1)[ n2 – n – 2]

                                = n(n-1)(n-2)(n+1)

                                =(n-2)(n-1)n(n+1)   … Product of 4 consecutive integers

We know that product of any four consecutive integer is divisible by 4 !

Thus, m2-2m is divisible by 24.

(ii) solution is :  HERE